Divisibility Squares Sudoku
(Published on 16. July 2020, 03:33 by ProwlingTiger)
I've had the idea of this puzzle for a long time, and it was extraordinarily difficult to implement - however, I've finally got one!
Normal sudoku rules apply. Additionally, every single 4x4 square in the grid has an even sum, and every single 7x7 square has a sum that is a multiple of 5. Lastly, each of the pink 2x2 squares also have an even sum.
To further clarify the rule, in the example sudoku grid below, all possible 3x3 squares (including the colored ones) have a sum that is divisible by 3. (There are 49 total possible 3x3 squares, all of which have sums divisible by 3.) For example, in the yellow square, 9+7+2+1+2+6+4+5+9=45 is divisible by 3.
And here is the real puzzle. I might post a file or a brief summary of the (in my opinion, really cool) strategies that I discovered, if I can figure out how.
Solution code: Row 5, then Column 4.
Comments
on 17. June 2021, 19:14 by polar
Magnificent puzzle! Very rewarding indeed :)
on 19. September 2020, 04:54 by harrison
ProwlingTiger--this was an incredibly unique and difficult puzzle. I was very pleased and relieved to have finally solved it!
on 18. August 2020, 10:55 by joecat
Really nice puzzle - thank you!
on 9. August 2020, 18:29 by Jesper
I thought this was an amazing puzzle, requiring very interesting and original logic. Not easy to figure out, but very rewarding!
on 17. July 2020, 10:57 by MagnusJosefsson
Very nice and original puzzle, thank you!
on 16. July 2020, 19:12 by emmettcito
Lovely puzzle :) How were you able to set something like this, as that seems like that would be quite a challenge.
on 16. July 2020, 14:29 by SudokuExplorer
Wow! What a lovely puzzle! There is some really nice logic if you think about the geometry of the constraints. Congratulations for making one with such a clean solution path!
on 16. July 2020, 05:40 by ProwlingTiger
@RockyRoer: Good idea. Thanks for doing the puzzle! And I will certainly check your puzzles out and give them my best shot!
on 16. July 2020, 05:39 by RockyRoer
I'd also add the arithmetics needed tag.
on 16. July 2020, 05:30 by ProwlingTiger
@Greg: It was just an example.
on 16. July 2020, 05:30 by RockyRoer
@Prowling Tiger:
I enjoyed this a lot. Definitely 'cheated' by using a solver to help eliminate the possibilities, but that was no easy feat as you still had to determine how to determine what combinations of cells were odd, even, multiples of 5, 10, etc, but I still think I earned the solve :-) Feel free to hide this if you think this was giving away too much of a hint, but it was an enjoyable puzzle for sure. I hope others will enjoy it too.
Shameless plug... If you like this puzzle, you'll probably enjoy mine too -- some of the same math tricks would work, but I definitely learned some new ones doing yours. https://logic-masters.de/Raetselportal/Raetsel/zeigen.php?id=0003U9
on 16. July 2020, 05:28 by Greg
Is the 3x3 always = 45 a rule that is used in the puzzle or did you just use it as a way of explaining the other rules?
on 16. July 2020, 04:25 by ProwlingTiger
Added title.
on 16. July 2020, 03:46 by RockyRoer
I hope you add a title to this so people can find it easier :-)
